Yes, foreigners can own property in Mexico. In 1994, amendments to the Constitution permitted foreigners to purchase and own real estate in Mexico located within the “restricted zone” which is all land within 60 miles of a national border and within 30 miles of the Mexican Coast. This Law permitted ownership through a land trust or “Fideicomiso”.
A “Fideicomiso” is a Mexican Trust. The way it works is the Mexican Government issues a permit to a Chartered Bank of your choice doing business in Mexico. This allows the bank to act as the Administrator for the owner of the property. The bank acts as the “Trustee” for the Trust and the Owner is the “Beneficiary” of the Trust. The “Beneficiary” rights are very similar to Living Wills or Estate Trusts in the U.S.
You have all the rights that an owner of property in the U.S. or Canada has, including the right to enjoy the property, sell the property, rent the property, improve the property, etc.